Suppose J(r) is constant in time but p (r, t) is not---conditions that might prevail, for instance, during the charging of a capacitor.

(a) Show that the charge density at any particular point is a linear function of time: p(r, t) = p(r, 0) + p(r, 0)t, where p(r, 0) is the time derivative of p at t = 0.

This is not an electrostatic or magnetostatic configuration;21 nevertheless--rather surprisingly??both Coulomb's law (in the form of Eq. 2.8) and the Biot-Savart law (Eq. 5.39) hold, as you can confirm by showing that they satisfy Maxwell's equations. In particular:

(b) Show that obeys Ampere's law with Maxwell's displacement current-term.

B(r) = J(r') x 4 f d